Graph each function. Give the domain and range. ƒ(x) = (log￬2 x) + 3

Logarithmic functions, such as f(x) = log₂(x), are the inverses of exponential functions. They are defined for positive real numbers, meaning the input x must be greater than zero. The base of the logarithm indicates the number that is raised to a power to obtain x. Understanding the properties of logarithms is essential for analyzing their graphs and determining their domains and ranges.

The domain of a function refers to all possible input values (x-values) that the function can accept, while the range refers to all possible output values (f(x)-values) that the function can produce. For the function f(x) = log₂(x) + 3, the domain is x > 0, and the range is all real numbers greater than 3. Identifying the domain and range is crucial for graphing functions accurately.

Graphing functions involves plotting points on a coordinate plane to visualize the relationship between the input and output values. For f(x) = log₂(x) + 3, the graph will show a logarithmic curve that shifts upward by 3 units. Understanding how to graph functions helps in interpreting their behavior and characteristics, such as asymptotes and intercepts.